Methods and electronic devices for obtaining information on a battery pack

ABSTRACT

Methods and electronic devices for estimating state of charge (SOC) of a battery pack. Various embodiments provide a model comprising an (electrical) equivalent circuit model, an electrochemical (thermal) model, and a (convective) thermal model. The model estimates parameters pertaining to each cell of the battery pack individually, and determines the variations in the values of the parameters among each of the cells of the battery pack. The parameters include capacity, temperature current, voltage, and SOC. The parameters are computed based on at current drawn by the battery pack, electrochemical parameters, thermal parameters, and cell internal and connection resistances of the individual cells. Various embodiments compute battery pack uptime, chargeable capacity of the battery pack and SOC of the battery pack, based on the values of the parameters.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is based on and claims priority under 35 U.S.C. § 119 to Indian Provisional Patent Application No. 202041010259, filed on Mar. 10, 2020, in the Indian Patent Office, and Indian Complete Patent Application No. 202041010259, filed on Nov. 30, 2020, in the Indian Patent Office the disclosures of which are incorporated by reference herein in their entireties.

BACKGROUND Field

The disclosure relates to Battery Management Systems (BMS), and for example, to methods and electronic devices for accurately estimating State of Charge (SOC), uptime and capacity of a battery pack.

Description of Related Art

A battery pack comprises a plurality of cells, wherein each cell can be connected to other cells in series or parallel. Currently, coulomb counting is being used for determining the State of Charge (SOC) of the battery pack. Coulomb counting typically considers the input current at the battery pack level, assuming that the current distribution across all cells of the battery pack is uniform and capacities of all cells in the battery pack are same.

These considerations, however, can introduce errors in the estimation of the SOC of the battery pack. This is because it is likely that there are variations in parameters such as capacities, resistances (internal and connection), temperatures (ambient and surface), SOC, and so on, amongst the cells of the battery pack. The variations in the parameters are magnified with increasing number of charge-discharge cycles. During the manufacturing of the battery pack, variations (tolerances) can be introduced in the components at the cell level. This can lead to further variations in the parameters. The cell-to-cell variations in the parameters lead to deviations in current flowing through each cell and voltage across the terminals of each cell, which can further introduce variations in the SOC and the capacities (State of Health (SOH)) amongst the cells of the battery pack.

The connectors, bolts and nuts, cables, and bus bars contribute to the overall resistance and impedance of the battery pack. These resistances can divert current, divide voltage, generate heat, and introduce additional factors (which may be non-linear) used for estimating the SOC of the battery pack. The additional impedances can be distributed non-uniformly across the cells of the battery pack. Therefore, the additional impedances can impact the accuracy of estimation of the SOC and the capacity of the battery pack. The cell-to-cell thermal variations, based on locations of the cells (a cell located in a corner is likely to have a lesser surface and ambient temperatures compared to a cell located in a center of the battery pack), can trigger voltage and capacity variations. The voltage and capacity variations can leads to redistribution of current amongst the cells of the battery pack, thereby affecting the distribution of charge across the individual cells, and SOC of individual cells in the battery pack and/or the SOC of the battery pack.

If multiple cells in the battery pack are connected in series, it is expected that the same current is passing through each of the cells. However, due to cell-to-cell variations in the parameters, the same current passing through all the cells may not translate into an equivalent range of SOC. There can also be cell-to-cell variations in voltage drop (even though the cells are connected in series). Similarly, if the multiple cells in the battery pack are connected in parallel, it is expected that the voltage across the terminals of each of the cells is same due to spontaneous internal balance. However, the internal balance may be affected by factors such as variations in cell internal resistance, which in turn affects the current distribution in the (parallel) branches (in which the cells are located).

In other existing methods, the remaining capacity and the chargeable capacity of the battery pack is determined based on the cell having the lowest capacity. This is because the cell having the lowest capacity is expected to discharge first, and when the cell (having the lowest capacity) discharges, it is considered that the cells connected in series with the discharged cell have ceased to function. This consideration can also lead to erroneous estimation of the SOC and the battery pack uptime, because there are conditions wherein a cell having higher capacity can discharge faster than the cell having the lowest capacity. If the cell having the lowest capacity is connected in parallel with other cells and is having a high internal resistance, the current flowing through the cell will be the lowest amongst the currents flowing through the other cells. Also, if the cell having the lowest capacity is connected in series with other cells, and if the busbar connection resistance of the cell is lower compared to the other cells, then a same amount of charge (current) passing through all cells can lead to lower voltage drop or SOC at the cell (having the lowest capacity). This will reduce the rate of discharge of the cell and expand the uptime of the cell, compared to the other cells having a higher capacity.

The errors in the estimations of the remaining capacity and the SOC of the battery pack can mislead a user. The impact of these errors is particularly significant at the end of the discharge cycles. Consider that the actual SOC of the battery pack is 1% and the SOC of the battery is computed as 12%. In this scenario, the user, while expecting the battery pack to function normally for a certain period of time (or preparing to charge the battery pack), may experience a sudden drop in the SOC of the battery pack and an unexpected/early shutdown of the equipment hosting the battery pack. Therefore, erroneous estimation of the remaining capacity and the SOC of the battery pack may impact the reliability of the battery pack, and consequently the user experience.

SUMMARY

Embodiments of the disclosure disclose methods and electronic devices for providing a model for more accurately estimating at least one of uptime of a battery pack, chargeable capacity of the battery pack, State of Charge (SOC) of the battery pack, voltage of the battery pack, temperature of the battery pack, and remaining capacity of the battery pack.

Embodiments of the disclosure perform the estimations using at least one of an equivalent circuit model, an electrochemical model, and a thermal model, wherein the equivalent circuit model, the electrochemical model, and the thermal model are coupled to each other.

Embodiments of the disclosure perform estimation in real time (online) or prior to termination of every discharge cycle, wherein the estimation is performed based on cell-to-cell variations in at least one parameter comprising voltage of a cell, SOC of the cell, capacity of the cell, current flowing through the cell, ambient temperature of the cell, and surface temperature of the cell.

Embodiments of the disclosure compute the voltage, current, SOC, temperature, capacity, and so on, of each of the cells of the battery pack based on at least one of current drawn by the battery pack, internal resistances, connection resistances, electrochemical parameters, and thermal parameters.

Embodiments of the disclosure provide methods and electronic devices for providing a model for accurately estimating uptime of a battery pack, remaining capacity of the battery pack available for discharge, chargeable capacity of the battery pack, and State of Charge (SOC) of the battery pack. Example embodiments include performing the estimations based on parameters pertaining to each of a plurality of cells in the battery pack. In various example embodiments, the battery pack comprises a plurality of modules connected in series, wherein each of the plurality of modules comprises a plurality of branches connected in parallel, wherein each of the plurality of branches comprises a cell. Various example embodiments include determining/identifying the variations in the parameters amongst each of the plurality of cells (in each of the plurality of branches) in each of the plurality of modules. In an embodiment, the parameters are SOC of a cell, capacity of the cell, voltage of the cell (branch), current flowing through the cell (branch), and ambient and surface temperatures of the cell.

Various example embodiments include determining/identifying the parameters pertaining to each of the cells based on operating current fed to the battery pack, electrochemical parameters, thermal parameters, internal resistance of the cell, and connection resistance of the cell. In various example embodiments, the parameters can be determined/identified using a model, wherein the model comprises an equivalent circuit model, an electrochemical model, and thermal model, wherein the equivalent circuit model, the electrochemical model, and the thermal model are coupled with each other.

Once the parameters have been determined/identified, various example embodiments may include estimating/obtaining the uptime of the battery pack, the remaining capacity of the battery pack available for discharge, the chargeable capacity of the battery pack, and the SOC of the battery pack. The uptime of the battery pack may be estimated based on the uptime of a cell. The uptime of the cell may be computed based on SOC of the cell, capacity of a battery cell, and current flowing through the cell. The value of the uptime of the cell is lowest amongst the values of uptimes of the plurality of cells in the plurality of branches of each of the plurality of modules. The remaining capacity of the battery pack may be estimated based on remaining capacity of a cell in a branch of a module. The value of the remaining capacity of the cell may be computed based on SOC of the cell, capacity of the cell, current flowing through the cell, and current flowing in all branches of the module. The value of the remaining capacity of the cell is lowest amongst the values of remaining capacities of a plurality of battery cells in the plurality of branches of each of the plurality of modules.

The chargeable capacity of the battery pack may be a chargeable capacity of a cell in a branch of a module. The value of the chargeable capacity of the cell may be computed based on SOC of the cell, capacity of the cell, current flowing through the cell, and current flowing in all branches of the module. The value of the chargeable capacity of the cell is lowest amongst values of chargeable capacities of a plurality of cells in the plurality of branches of each of the plurality of modules. The SOC of the battery pack may be estimated based on the remaining capacity of the battery pack and the total capacity of the battery pack.

These and other aspects of the various example embodiments herein will be better appreciated and understood when considered in conjunction with the following description and the accompanying drawings. It should be understood, however, that the following descriptions, while indicating various example embodiments and numerous specific details thereof, are given by way of illustration and not of limitation. Many changes and modifications may be made within the scope of the example embodiments herein without departing from the spirit thereof, and the embodiments herein include all such modifications.

BRIEF DESCRIPTION OF THE DRAWINGS

The above and other aspects, features and advantages of certain embodiments of the present disclosure will be more apparent from the following detailed description, taken in conjunction with the accompanying drawings, in which:

FIG. 1 is a diagram illustrating an example battery pack comprising ‘S’ modules, wherein each module comprises ‘P’ branches, wherein uptime, State of Charge (SOC), and capacity of the battery pack are determined based on parameters pertaining to individual cells of the battery pack, according to various embodiments;

FIG. 2 is a block diagram illustrating an example Battery Management System (BMS) configured to predict capacity and SOC of a battery pack 205, according to various embodiments;

FIG. 3 is a flowchart illustrating an example method for estimating capacity and SOC of a battery pack based on variations of parameters pertaining to battery cells of the battery pack, according to various embodiments;

FIG. 4 is a diagram illustrating an example model for estimation of parameters pertaining to the individual cells of the battery pack, according to various embodiments; and

FIG. 5 is a diagram illustrating an example battery pack comprising three modules, wherein each of the three modules comprises two branches, according to various embodiments.

DETAILED DESCRIPTION

Various example embodiments and various features and advantageous details thereof are explained in greater detail below with reference to the non-limiting example embodiments illustrated in the accompanying drawings and described in the following disclosure. Descriptions of well-known components and processing techniques may be omitted so as to not unnecessarily obscure the example embodiments herein. The examples used herein are intended merely to facilitate an understanding of ways in which the various example embodiments herein may be practiced and to further enable those of skill in the art to practice the various example embodiments herein. Accordingly, the examples should not be construed as limiting the scope of the various example embodiments herein.

Various example embodiments herein disclose methods and systems for providing a model for accurately estimating at least one of State of Charge (SOC) of a battery pack, battery pack uptime, chargeable capacity of the battery pack, voltage of the battery pack, temperature of the battery pack, and remaining capacity of the battery pack. Various embodiments include performing the estimations using, for example, and without limitation, an equivalent circuit model, an electrochemical model, and a thermal model. The equivalent circuit model, the electrochemical model, and the thermal model may be coupled to each other. The estimation can be performed in real time (online) or prior to termination of every discharge cycle. The various example embodiments consider variations in at least one parameter pertaining to each cell of the battery pack comprising voltage of a cell, SOC of the cell, capacity of the cell, current flowing through the cell, ambient temperature of the cell, and surface temperature of the cell. Various embodiments include computing the voltage, current, SOC, temperature, capacity, and so on, of each of the cells of the battery pack based on at least one of current drawn by the battery pack, internal and connection resistances of the cells, electrochemical parameters, and thermal parameters. Various example embodiments include estimating the SOC of the battery pack, battery pack uptime, chargeable capacity of the battery pack, and remaining capacity of the battery pack, based on the computed values of voltage, current, SOC, temperature, capacity, and so on, of each of the cells of the battery pack.

Referring now to the drawings, and more particularly to FIGS. 1, 2, 3, 4 and 5, where similar reference numerals refer to corresponding features consistently throughout the figures, there are shown various example embodiments.

FIG. 1 is a diagram illustrating an example battery pack comprising ‘S’ modules, wherein each module comprises ‘P’ branches, wherein uptime, SOC, and capacity of the battery pack are determined based on parameters pertaining to individual cells of the battery pack, according to various embodiments. As illustrated in FIG. 1, each branch of a module includes a cell. As there are ‘S’ modules and ‘P’ branches in each module, the cells in the first module can be labeled as Cell-11, Cell-12, . . . , and Cell-1P. Similarly, the cells in the S^(th) module can be labeled as Cell-S1, Cell-S2, . . . , and Cell-SP. Each cell has an internal resistance. The resistances of the cell in the first module can be labeled as r₁₁, r₁₂, . . . , and rip. Similarly, the cells in the S^(th) module can be labeled as r_(S1), r_(S2), . . . , and r_(SP).

The modules may be referred to as units of the battery pack connected in series. For the sake of simplicity, the charging current passing through the all the modules is assumed to be same. However, there can be differences in voltage drop across the terminals of the battery pack, e.g., the distribution of voltage amongst the modules of battery pack can be non-uniform. The voltage across the terminals of the cells in a module can be different. There can be variations in temperature, SOC, capacity, internal resistance, busbar resistance, and so on, amongst the cells in the branches of each of the modules of battery pack. These variations can cause variations in the voltage drop across the terminals of the branches in each of the modules, and variations in the current flowing through the different branches in each of the modules of the battery pack. The currents flowing through the different branches of the first module are labeled as i₁₁, i₁₂, . . . , and i_(1P). Similarly, the currents flowing through the different branches of the S^(th) module can be labeled as i_(S1), i_(S2), . . . , and i_(SP). The variations in voltage and current can impact remaining and chargeable capacities of the battery pack.

Various example embodiments include determining/identifying the parameters pertaining to the individual cells of the battery pack such as current (i_(jk), j→1-S, and k→1-P), SOC, capacity, voltage, ambient temperature, and surface temperature. The parameters pertaining to each cell of the battery pack can be determined based on operating current fed to the battery pack (i), internal resistance of the cell, connection resistance of the cell, electrochemical parameters and thermal parameters.

Various example embodiments include determining/obtaining the uptime of the battery pack, the remaining capacity of the battery pack, the chargeable capacity of the battery pack, and the SOC of the battery pack; based on variations in the parameters pertaining to the individual cells (such as cell-jk, wherein j→1-S and k→1-P) of the battery pack. In an embodiment, the parameters are capacities of the individual cells, current passing through the individual cells (i_(jk)), and the SOC of the individual cells (SOC_(jk)).

The uptime of the battery pack may be computed based on SOC of a cell in the battery pack, capacity of the battery cell, and current flowing through the cell. Consider that the cell is cell-jk, wherein SOC_(jk) (j→1-S and k→1-P) is the SOC of the cell, Q_(k) (j→1-S and k→1-P) is the capacity of the cell, and i_(jk) (j→1-S and k→1-P) is the current flowing through the cell. The uptime of a module of the battery pack, in which the cell-jk is located, may be:

$\begin{matrix} {{{Uptime}\mspace{14mu}({module})} = {\min_{1 \leq k \leq P}\left( \frac{{SOC}_{jk}Q_{jk}}{i_{jk}} \right)}} & \left( {{Equation}\text{-}1} \right) \end{matrix}$

The cell-jk is located in a branch ‘k’ of a module ‘j’. The value of uptime of the module ‘j’ is the lowest value of uptime amongst the ‘P’ values of uptimes of ‘P’ cells in the ‘P’ branches of the module ‘j’. In this equation (equation 1), the value of uptime of the cell in the k^(th) branch in module ‘j’ is the lowest amongst the uptimes of the ‘P’ cells in the ‘P’ branches of the module ‘j’.

The uptime of the battery pack may be given as:

$\begin{matrix} {{{Uptime}\mspace{14mu}({pack})} = {\min_{1 \leq j \leq S}\left\{ {\min_{1 \leq k \leq P}\left( \frac{{SOC}_{jk}Q_{jk}}{i_{jk}} \right)} \right\}}} & \left( {{Equation}\text{-}2} \right) \end{matrix}$

The value of the uptime of the module ‘j’ is the lowest amongst the ‘S’ values of uptimes of ‘S’ modules in the battery pack. It can be observed, as per equation 2, that uptime of the cell-jk is the uptime of the battery pack, as the uptime of the cell-jk is the lowest amongst the uptimes of all cells in ‘P’ branches of each of the ‘S’ modules of the battery pack.

The remaining capacity of the battery pack may be computed based on SOC of a cell in the battery pack, capacity of the battery cell, current flowing through the cell and, current flowing in all branches of the module in which the cell is located. Consider that the cell is cell-jk, wherein SOC_(jk) (j→1-S and k→1-P) is the SOC of the cell, Q_(k) (j→1-S and k→1-P) is the capacity of the cell, and i_(jk) (j→1-S and k→1-P) is the current flowing through the cell. The remaining capacity of a module of the battery pack, in which the cell-jk is located, is given as:

$\begin{matrix} {{{Rem}\mspace{14mu}{Cap}\mspace{14mu}({module})} = {\min\limits_{1 \leq k \leq P}{\left( \frac{{SOC}_{jk}Q_{jk}}{i_{jk}} \right)\left( {\sum_{k = 1}^{P}i_{jk}} \right)}}} & \left( {{Equation}\text{-}3} \right) \end{matrix}$

The summation represents the current flowing through the ‘P’ branches of the module ‘j’. The cell-jk is located in a branch ‘k’ of a module ‘j’. The value of remaining capacity of the module ‘j’ is the lowest value of remaining capacity amongst the ‘P’ values of remaining capacities of ‘P’ cells in the ‘P’ branches of the module ‘j’. In this equation the value of remaining capacity of the cell in the k^(th) branch in module ‘j’ is the lowest amongst the ‘P’ cells in the ‘P’ branches of the module ‘j’. The remaining capacity of the battery pack is given as:

$\begin{matrix} {{{Rem}\mspace{14mu}{Cap}\mspace{14mu}({pack})} = {\min\limits_{1 \leq j \leq S}\left\{ {\min_{1 \leq k \leq P}{\left( \frac{{SOC}_{jk}Q_{jk}}{i_{jk}} \right)\left( {\sum_{k = 1}^{P}i_{jk}} \right)}} \right\}}} & \left( {{Equation}\text{-}4} \right) \end{matrix}$

The value of the remaining capacity of the module ‘j’ is the lowest amongst the ‘S’ values of remaining capacities of ‘S’ modules in the battery pack. It can be observed, as per equation 4, that remaining capacity of the cell-jk is the remaining capacity of the battery pack, as the remaining capacity of the cell-jk is the lowest amongst the remaining capacities of all cells in ‘P’ branches of each of the ‘S’ modules of the battery pack.

The chargeable capacity of the battery pack may be computed based on SOC of a cell in the battery pack, capacity of the battery cell, current flowing through the cell and, current flowing in all branches of the module in which the cell is located. Consider that the cell is cell-jk, wherein SOC_(jk) (j→1-S and k→1-P) is the SOC of the cell, Q_(jk) (j→1-S and k→1-P) is the capacity of the cell, and i_(jk) (j→1-S and k→1-P) is the current flowing through the cell. The chargeable capacity of a module of the battery pack, in which the cell-jk is located, is given as:

$\begin{matrix} {{{Crg}\mspace{14mu}{Cap}\mspace{14mu}({module})} = {\min\limits_{1 \leq k \leq S}{\begin{pmatrix} {1 - {SOC}_{jk}} \\ i_{jk} \end{pmatrix}{Q_{jk}\left( {\sum_{k = 1}^{P}i_{jk}} \right)}}}} & \left( {{Equation}\text{-}5} \right) \end{matrix}$

The summation represents the current flowing through the ‘P’ branches of the module ‘j’. The cell-jk is located in a branch ‘k’ of a module ‘j’. The value of chargeable capacity of the module ‘j’ is the lowest value of chargeable capacity amongst the ‘P’ values of chargeable capacities of ‘P’ cells in the ‘P’ branches of the module ‘j’. In this equation the value of chargeable capacity of the cell in the k^(th) branch in module ‘j’ is the lowest amongst the ‘P’ cells in the ‘P’ branches of the module ‘j’. The chargeable capacity of the battery pack is given as:

$\begin{matrix} {{{Crg}\mspace{14mu}{Cap}\mspace{14mu}({pack})} = {\min\limits_{1 \leq k \leq S}\left\{ {\min_{1 \leq k \leq P}{\left( \frac{1 - {SOC}_{jk}}{i_{jk}} \right){Q_{jk}\left( {\sum_{k = 1}^{P}i_{jk}} \right)}}} \right\}}} & \left( {{Equation}\text{-}6} \right) \end{matrix}$

The value of the chargeable capacity of the module ‘j’ is the lowest amongst the ‘S’ values of chargeable capacities of ‘S’ modules in the battery pack. It can be observed, as per equation 4, that remaining capacity of the cell-jk is the chargeable capacity of the battery pack, as the chargeable capacity of the cell-jk is the lowest amongst the chargeable capacities of all cells in ‘P’ branches of each of the ‘S’ modules of the battery pack.

The SOC of the battery pack may be determined based on the remaining capacity of the battery pack and the total capacity of the battery pack. The SOC of the battery pack is given as:

$\begin{matrix} {{{SoC}({pack})} = {\min_{1 \leq k \leq S}{\left\{ {\min_{1 \leq k \leq P}{\left( \frac{{SOC}_{jk}Q_{jk}}{i_{jk}} \right)\left( {\sum_{k = 1}^{P}i_{jk}} \right)}} \right\}/Q_{pack}^{d}}}} & \left( {{Equation}\text{-}7} \right) \end{matrix}$

FIG. 2 is a block diagram illustrating an example Battery Management System (BMS) 200 configured to predict capacity and SOC of a battery pack 205, according to various embodiments. As illustrated in FIG. 2, the BMS 200 includes a Power Management Integrated Circuit (PMIC) 201. The PMIC 201 includes a processor (e.g., including processing circuitry) 202, a memory 203 and a display 204. The BMS 200 is hosted in a device (not shown), which includes the battery pack 205. The battery pack 205 may include a plurality of cells, wherein the plurality of cells can be arranged in series and/or parallel. In an embodiment, the battery pack 205 comprises a plurality of modules connected in series, wherein each module comprises a plurality of cells connected in parallel. Examples of the device, hosting the BMS 200, may include, but are not limited to, an electronic device, a portable device, a mobile device/phone, a robot, an Uninterrupted Power Supply (UPS), a solar panel, an electric vehicle, a personal computer, a laptop, and so on.

The BMS 200 is configured to accurately estimate the SOC of the battery pack 205, even if there are significant variations between the capacities of the individual cells of the battery pack 205. The BMS 200 is configured to estimate remaining capacity and uptime of the battery pack 205, for determining the time period for which a user can expect to operate the device without interruption and to avoid possible failures during runtime (execution of an instruction). The BMS 200 is configured to determine the chargeable capacity of the battery pack 205. The BMS 200 is configured to consider variations of SOC, temperature, capacity, voltage, current, ambient temperature, and surface temperature of each of the individual cells of the battery pack 205, during the estimation of the SOC of the battery pack 205, the remaining capacity of the battery pack 205, the chargeable capacity of the battery pack 205, and the uptime of the battery pack 205.

The BMS 200 is configured to estimate the voltage drop across the terminals of each of the individual cells of the battery pack 205, and current flowing through each of the individual cells. The BMS 200 is configured to estimate the ambient and surface temperatures of each of the individual cells of the battery pack 205. The BMS 200 is configured to estimate SOC of each of the individual cells and the cell capacity of each of the individual cells. The estimations may, for example, be performed based on operating current fed to the battery pack 205, electrochemical parameters, thermal parameters, internal resistances of each of the individual cells of the battery pack 205, and connection resistances of each of the individual cells of the battery pack 205.

In an embodiment, the processor 202 may include various processing circuitry and may estimate the SOC, the capacity, the voltage, the current, the ambient temperature, and the surface temperature of each of the individual cells of the battery pack 205, using a physics based model. The model comprises three sub-models, including, for example, and without limitation, an (electrical) equivalent circuit model, a (convective) thermal model, and a (cell reduced order) electrochemical (thermal) model. The sub-models may be fully coupled with each other. The thermal model operates at the battery pack level. The electrochemical model operates at the cell (cells of the battery pack 205) level. Each of the sub-models can receive inputs, which include parameters that are generated as outputs by other sub-models. The sub-models can receive the operating current fed to the battery pack 205, electrochemical parameters, thermal parameters, internal resistances of each of the individual cells of the battery pack 205, and connection resistances of each of the individual cells of the battery pack 205, as inputs.

For a particular cell, the equivalent circuit model receives the charging current (current fed to the battery pack 205), internal resistances of the cell, and connection resistance (contributed by the connectors, bolts and nuts, cables, and bus bars) of the cell as inputs. The equivalent circuit model further receives the voltage of the cell, from the electrochemical model, as an input. The electrochemical model receives electrochemical parameters (comprising of electrode level information such as length, particle radius, active material loading capacities, diffusion characteristics, and so on) as input. The electrochemical model further receives the current flowing through the cell from the equivalent circuit model, and the ambient temperature of the cell from the thermal model, as inputs. The thermal model receives thermal parameters (comprising of heat transfer coefficients and cooling fluid material properties such as density, specific heat capacity, and so on) as input. The thermal model further receives the surface temperature of the cell from the electrochemical model as an input.

The equivalent circuit model generates the current flowing through the cell as output. The current flowing through the cell is used by the electrochemical model as input, to predict the voltage of the cell as output, estimate the SOC of the cell, and estimate the capacity of the cell. The cell voltage is used as an input, by the equivalent circuit model, to calculate the voltage drop across the terminals and generating the current flowing through the cell as output. Therefore, the equivalent circuit model and the electrochemical model are coupled with each other.

The thermal model generates the ambient temperature of the cell as output, which is used by the electrochemical model as input to generate the surface temperature of the cell as output. The surface temperature of the cell is used as input, by the thermal model, to generate the ambient temperature of the cell as output. Therefore, the thermal model and the electrochemical model are coupled with each other.

The current flowing through the individual cells, the voltage drop across the terminals of the individual cells, the ambient temperature of the individual cells, surface temperature of the individual cells, act as internal input parameters and external input parameters. The charging current, internal resistances of the individual cells, connection resistances, electrochemical parameters, and thermal parameters, are the (external) inputs of the model, which are received as inputs by the sub-models (the equivalent circuit model, the electrochemical model, and the thermal model).

The processor 202 may estimate the SOC of the battery pack 205, the remaining capacity of the battery pack 205, the chargeable capacity of the battery pack 205, and the uptime of the battery pack 205, based on the estimated values of capacity, SOC, voltage, current, and ambient and surface temperatures of each of the individual cells of the battery pack 205.

In an embodiment, the processor 202 may estimate the uptime of the battery pack 205 based on the uptime of a cell in the battery pack 205. The uptime of the cell is determined based on SOC of a cell, capacity of the cell, and current flowing through the cell. The value of the uptime of the cell is lowest amongst values of uptimes of a plurality of battery cells in the plurality of branches of each of the plurality of modules.

In an embodiment, the processor 202 may estimate the remaining capacity of the battery pack 205 based on the remaining capacity of a cell battery pack 205. The remaining capacity of the cell is computed based on SOC of the cell, capacity of the cell, current flowing through the cell, and current flowing in all branches of the module in which the cell is located. The value of the remaining capacity of the cell is lowest amongst values of remaining capacities of a plurality of battery cells in the plurality of branches of each of the plurality of modules. In an embodiment, the processor 202 may estimate the SOC of the battery pack 205, based on the remaining capacity of the battery pack 205 and the total capacity of the battery pack 205.

In an embodiment, the processor 202 may estimate the chargeable capacity of the battery pack 205 based on the chargeable capacity of a cell battery pack 205. The chargeable capacity of the cell may be computed based on SOC of the cell, capacity of the cell, current flowing through the cell, and current flowing in all branches of the module in which the cell is located. The value of the chargeable capacity of the cell is lowest amongst the values of chargeable capacities of a plurality of battery cells in the plurality of branches of each of the plurality of modules.

FIG. 2 illustrates various example units of the BMS 200, but it is to be understood that other embodiments are not so limited. In other embodiments, the BMS 200 may include less or more number of units. Further, the labels or names of the units of the BMS 200 are used simply for illustrative purposes and do not limit the scope of the disclosure. One or more units can be combined together to perform same or substantially similar function in the BMS 200.

FIG. 3 is a flowchart 300 illustrating an example method for estimating capacity and SOC of the battery pack 205 based on variations of parameters pertaining to battery cells of the battery pack 205, according to various embodiments. At operation 301, the method includes determining at least one value of at least one parameter pertaining to each of a plurality of battery cells in the battery pack 205. The at least one parameter pertaining to a battery cell, among the plurality of battery cells, includes, for example, and without limitation, SOC of the battery cell, capacity of the battery cell, voltage of the battery cell, current flowing through the battery cell, ambient temperature of the battery cell, surface temperature of the battery cell, etc. Various embodiments include determining the at least one parameter pertaining to a battery cell based on operating current fed to the battery pack 205, at least one electrochemical parameter fed to the battery pack 205, at least one thermal parameter fed to the battery pack 205, internal resistance of the battery cell, and connection resistance of the battery cell.

In an embodiment, the at least one parameter may be determined using a model, including a plurality of fully coupled models. The sub-models may include, for example, and without limitation, an equivalent circuit model, an electrochemical model, and a thermal model. The sub-models can receive, as inputs, the operating current fed to the battery pack 205, the at least one electrochemical parameter, the at least one thermal parameter, the internal resistances of the battery cells of the battery pack 205, and connection resistances of the battery cells battery pack 205. The sub-models may determine the at least one value of the at least one parameter (operating current fed to the battery pack 205, the at least one electrochemical parameter, the at least one thermal parameter, internal resistance of the battery cell, and connection resistance of the battery cell) pertaining to each of a plurality of battery cells in the battery pack 205 based on the inputs.

The sub-models of the model may be coupled based on inputs and outputs exchanged between the sub-models. A first parameter generated as an output by a first sub-model may be used by a second sub-model as an input. A second parameter generated as an output by the second sub-model may be used by the first sub-model as an input. For example, the equivalent circuit model may receive the voltage of the individual cells, from the electrochemical model. The electrochemical model may receive the current flowing through the individual cells from the equivalent circuit model, and ambient temperature from the thermal model, as inputs. The thermal model may receive the surface temperature of the individual cells from the electrochemical model as an input.

At operation 302, the example method includes computing at least one of an uptime of the battery pack 205, a remaining capacity of the battery pack 205, a chargeable capacity of the battery pack 205, and an SOC of the battery pack 205 based on variations in the at least one parameter among the plurality of battery cells in the battery pack. Consider that the battery pack comprises a plurality of modules connected in series. Each of the plurality of modules may include a plurality of branches connected in parallel, wherein each of the plurality of branches comprises a battery cell. Various embodiments include determining at least one of SOC, capacity, voltage, current, and ambient and surface temperatures, of each of the battery cells in the plurality of branches of each of the plurality of modules, using the model.

Once the parameters (SOC, capacity, voltage, current, ambient temperature, and surface temperature) pertaining to each of the battery cells have been determined using the model, various embodiments include computing the uptime of the battery pack 205, the remaining capacity of the battery pack 205, the chargeable capacity of the battery pack 205, and the SOC of the battery pack.

The uptime of the battery pack 205 may be the uptime of a battery cell in a branch of a module. For a particular branch in a module, various embodiments include computing a product of capacity of the battery cell and SOC of the battery cell. Various embodiments include obtaining a ratio of the product and the current flowing through the battery cell. Various embodiments include computing the ratios for each of the battery cells in each of the branches of the module. The ratio with the lowest value can be considered as the uptime of the module. Similarly, various embodiments include computing the uptimes of each of the plurality of modules. The lowest value of uptime, among the values of the uptimes of each of the plurality of modules, is considered as the uptime of the battery pack 205.

The remaining capacity of the battery pack 205 may be the remaining capacity of a battery cell in a branch of a module. For a particular branch in a module, various embodiments include computing a product of the uptime of the battery cell in the branch and the summation of currents in each of the plurality of branches in the module. Various embodiments include computing the products for each of the plurality of branches in the module. The values of the products represent the remaining capacities of the battery cells in the plurality of branches of the module. The product with the lowest value can be considered as the remaining capacity of the module. Similarly, various embodiments include determining the remaining capacities of each of the plurality of modules. The lowest value of remaining capacity, amongst the values of the remaining capacities of each of the plurality of modules, is considered as the remaining capacity of the battery pack 205.

The chargeable capacity of the battery pack 205 may be the chargeable capacity of a battery cell in a branch of a module. For a particular branch in a module, various embodiments include computing a ratio of capacity of the battery cell in the branch and the current passing through the branch. Various embodiments include computing a difference between the ratio and the uptime of the battery cell in the branch. Various embodiments include computing a product of the difference and the summation of currents in each of the plurality of branches in the module. Similarly, various embodiments include computing the products for each of the plurality of branches in the module. The values of the products represent the chargeable capacities of the battery cells in the plurality of branches of the module. The product with the lowest value can be considered as the chargeable capacity of the module. Similarly, various embodiments include determining the chargeable capacities of each of the plurality of modules. The lowest value of chargeable capacity, among the values of the chargeable capacities of each of the plurality of modules, is considered as the chargeable capacity of the battery pack 205.

The SOC of the battery pack 205 may be determined based on a ratio of the remaining capacity of the battery pack 205 and the original capacity of the battery pack 205.

The various actions in the flowchart 300 may be performed in the order presented, in a different order, or simultaneously. Further, in some embodiments, some actions listed in FIG. 3 may be omitted.

FIG. 4 is a diagram illustrating an example model for estimation of parameters pertaining to the individual cells of the battery pack 205, according to various embodiments. As illustrated in FIG. 4, the model may include three sub-models, including, for example, an electrical equivalent circuit model, a convective thermal model, and a cell reduced order electrochemical-thermal model. The model may, for example, be configured to estimate the SOC of each of the individual cells, the capacity of each of the individual cells, the voltage drop across the terminals of each of the individual cells, the current flowing through each of the individual cells, and the ambient and surface temperatures of each of the individual cells.

The model may receive the applied current (I_(app)) or operating current, electrochemical parameters, thermal parameters, internal resistances of each of the individual cells, and connection resistances of each of the individual cells, as inputs. The electrical equivalent circuit model receives the applied current, the internal resistances and the connection resistances of each of the individual cells. The cell reduced order electrochemical-thermal model receives the electrochemical parameters. The convective thermal model receives the thermal parameters as input.

The sub-models, e.g., the electrical equivalent circuit model, the convective thermal model, and the cell reduced order electrochemical-thermal model are coupled with each other. The coupling may be based on a first sub-model receiving an input from a second sub-model, to generate an output. The generated output is received by the second sub-model to generate an output. For example, the electrical equivalent circuit model receives the voltage (φ_(jk)) of a cell (cell-jk) from the cell reduced order electrochemical-thermal model, as input. The cell reduced order electrochemical-thermal model receives the current flowing through the cell-jk (i_(jk)) from the electrical equivalent circuit model, and the ambient temperature (T_(amb)) of the cell-jk from the convective thermal model, as inputs. The cell reduced order electrochemical-thermal model generates the capacity and the SOC. The convective thermal model receives the surface temperature (T_(jk)) of the cell-jk from the cell reduced order electrochemical-thermal model as an input.

Based on the estimates of the SOC, capacity, voltage, current, and ambient and surface temperatures, of the individual cells of the battery pack 205, derived by the model, various embodiments include determining the uptime of the battery pack 205, the SOC of the battery pack 205, the remaining capacity of the battery pack 205, and the chargeable capacity of the battery pack 205.

FIG. 5 is a diagram illustrating an example battery pack comprising of three modules, wherein each of the three modules comprises two branches, according to various embodiments. As illustrated in FIG. 5, each branch of a module includes a cell. As there are three modules in the battery pack and two branches in each module, the cells in the first module can be labeled as Cell-1-1 and Cell-1-2. Similarly, the cells in the second module can be labeled as Cell-2-1 and Cell-2-2, and the cells in the third module can be labeled as Cell-3-1 and Cell-3-2. The resistances of the cells in the first module are labeled as r₁₁ and r₁₂. The resistances of the cells in the second module are labeled as r₂₁ and r₂₂. The resistances of the cells in the third module are labeled as r₃₁ and r₃₂.

The battery pack model may determine variations in temperature, SOC, capacity, internal resistance, busbar resistance, voltage, and current, amongst the six cells in six branches of the three modules of battery pack. The battery pack model determines the currents flowing through the two branches of each of the three modules. The currents are labeled as i₁₁, i₁₂, i₂₁, i₂₂, i₃₁, and i₃₂. The battery pack model may determine the uptime of the battery pack, the remaining capacity of the battery pack, the chargeable capacity of the battery pack, and the SOC of the battery pack; based on variations in the temperature, SOC, capacity, internal resistance, busbar resistance, voltage, and current, amongst the six cells in six branches of the three modules of battery pack.

The uptime of the battery pack is given as:

${{Uptime}\mspace{14mu}\underset{1 \leq j \leq 3}{({pack})}} = {\min\left\{ {\min\limits_{1 \leq k \leq 2}\left( \frac{{SOC}_{jk}Q_{jk}}{i_{jk}} \right)} \right\}}$

The remaining capacity of the battery pack is given as:

${{Rem}\mspace{14mu}{Cap}\mspace{14mu}({pack})} = {\min\limits_{1 \leq j \leq 3}\left\{ {\min\limits_{1 \leq k \leq 2}{\left( \frac{{SOC}_{jk}Q_{jk}}{i_{jk}} \right)\left( {\sum\limits_{k = 1}^{2}i_{jk}} \right)}} \right\}}$

The chargeable capacity of the battery pack is given as:

${{Crg}\mspace{14mu}{Cap}\mspace{14mu}({pack})} = {\min\limits_{1 \leq j \leq 3}\left\{ {\min\limits_{1 \leq k \leq 2}{\left( \frac{1 - {SOC}_{jk}}{i_{jk}} \right){Q_{jk}\left( {\sum\limits_{k = 1}^{2}i_{jk}} \right)}}} \right\}}$

The SOC of the battery pack is determined based on the remaining capacity of the battery pack and the total capacity of the battery pack. The SOC of the battery pack is given as:

${{SoC}({pack})} = {\min\limits_{1 \leq j \leq 3}{\left\{ {\min\limits_{1 \leq k \leq 2}{\left( \frac{{SOC}_{jk}Q_{jk}}{i_{jk}} \right)\left( {\sum_{k = 1}^{2}i_{jk}} \right)}} \right\}/Q_{pack}^{d}}}$

Various embodiments disclosed herein can be implemented through at least one software program running on at least one hardware device and performing network management functions to control the network elements. The network elements shown in FIG. 2 include blocks which can be at least one of a hardware device, or a combination of hardware device and software module.

Various example embodiments disclosed herein describe methods and systems for providing a model for accurately estimating battery pack uptime, remaining capacity of the battery pack available for discharge, and chargeable capacity of the battery pack. Therefore, it is understood that the scope of the disclosure is extended to such a program and in addition to a computer readable medium having a message therein, such computer readable storage medium may contain program code for implementation of one or more steps of the method, when the program runs on a server or mobile device or any suitable programmable device. The method may be implemented in example embodiment through or together with a software program written in example Very high speed integrated circuit Hardware Description Language (VHDL), or any other programming language, or implemented by one or more VHDL or several software modules being executed on at least one hardware device. The hardware device can be any kind of portable device that can be programmed. The device may also include hardware, for example, an Application-specific Integrated Circuit (ASIC), or a combination of hardware and software, for example, an ASIC and a Field Programmable Gate Array (FPGA), and/or at least one microprocessor and at least one memory with software modules located therein. The various example embodiments described herein may be implemented partly in hardware and partly in software. Various embodiments may be implemented on different hardware devices, e.g. using a plurality of Central Processing Units (CPUs).

The foregoing description of various example embodiments discloses the various embodiments herein so that others can, by applying current knowledge, readily modify and/or adapt for various applications such various embodiments without departing from the concept, and, therefore, such adaptations and modifications should and are intended to be comprehended within the meaning and range of equivalents of the disclosed embodiments. It is to be understood that the phraseology or terminology employed herein is for the purpose of description and not of limitation. Therefore, while various example embodiments herein have been described in terms of example embodiments, those skilled in the art will recognize that the various example embodiments herein can be practiced with modification within the scope of the embodiments as described herein. 

What is claimed is:
 1. A method for obtaining information on a battery pack by an electronic device, the method comprising: identifying, by the electronic device, at least one value of at least one parameter pertaining to each of a plurality of battery cells in the battery pack; and obtaining, by the electronic device, at least one of an uptime of the battery pack, a remaining capacity of the battery pack and a chargeable capacity of the battery pack, based on variations in the at least one value of the at least one parameter among the plurality of battery cells in the battery pack.
 2. The method, as claimed in claim 1, wherein the at least one value of the at least one parameter is identified, by the electronic device, using a model, wherein the model comprises an equivalent circuit model, an electrochemical model, and a thermal model, wherein the equivalent circuit model, the electrochemical model, and the thermal model are coupled.
 3. The method, as claimed in claim 1, wherein the at least one parameter pertaining to a battery cell, among the plurality of battery cells comprises a State of Charge (SOC) of the battery cell, capacity of the battery cell, voltage drop across terminals of the battery cell, current flowing through the battery cell, ambient temperature of the battery cell, and surface temperature of the battery cell.
 4. The method, as claimed in claim 1, wherein the at least one value of the at least one parameter pertaining to a battery cell, among the plurality of battery cells, is identified based on at least one of operating current fed to the battery pack, at least one electrochemical parameter fed to the battery pack, at least one thermal parameter fed to the battery pack, internal resistance of the battery cell, and connection resistance of the battery cell.
 5. The method, as claimed in claim 1, wherein the battery pack comprises a plurality of modules connected in series, wherein each of the plurality of modules comprises a plurality of branches connected in parallel, wherein each of the plurality of branches comprises a battery cell.
 6. The method, as claimed in claim 3, wherein the uptime of the battery pack includes an uptime of a battery cell in a branch of a module, wherein a value of the uptime of the battery cell is lowest among values of uptimes of a plurality of battery cells in the plurality of branches of each of the plurality of modules, wherein the value of the uptime of the battery cell is based on the SOC of the battery cell, capacity of the battery cell, and current flowing through the battery cell.
 7. The method, as claimed in claim 3, wherein the remaining capacity of the battery pack includes a remaining capacity of a battery cell in a branch of a module, wherein a value of the remaining capacity of the battery cell is lowest among values of remaining capacities of a plurality of battery cells in the plurality of branches of each of the plurality of modules, wherein the value of the remaining capacity of the battery cell is based on the SOC of the battery cell, capacity of the battery cell, current flowing through the battery cell, and current flowing in all branches of the module.
 8. The method, as claimed in claim 3, wherein the chargeable capacity of the battery pack includes a chargeable capacity of a battery cell in a branch of a module, wherein value of the chargeable capacity of the battery cell is lowest among values of chargeable capacities of a plurality of battery cells in the plurality of branches of each of the plurality of modules, wherein the value of the chargeable capacity of the battery cell is based on the SOC of the battery cell, capacity of the battery cell, current flowing through the battery cell, and current flowing in all branches of the module.
 9. The method, as claimed in claim 1, wherein the method further comprises computing, by the electronic device, a State of Charge (SOC) of the battery pack, based on the remaining capacity of the battery pack and a total capacity of the battery pack.
 10. A method for obtaining information on a battery pack by an electronic device, the method comprising: measuring a capacity of the battery pack by considering input local current variations that occur during charging and discharge operations due to variations in cell internal resistances, capacities, and cell-to-cell temperatures; calculating local cell currents using an electrical equivalent circuit model; calculating real time cell capacities and State of Charges (SOCs) using a cell electro-chemical and thermal model; and estimating a battery pack uptime, a usable capacity and a chargeable capacity of the battery pack using a physics based model to determine SOC of the battery pack.
 11. An electronic device comprising: a battery pack; and at least one processor configured to: identify at least one value of at least one parameter pertaining to each of a plurality of battery cells in the battery pack; and obtain at least one of an uptime of the battery pack, a remaining capacity of the battery pack and a chargeable capacity of the battery pack, based on variations in the at least one value of the at least one parameter among the plurality of battery cells in the battery pack.
 12. The electronic device as claimed in claim 11, wherein the at least one value of the at least one parameter is identified, by the at least one processor, using a model, wherein the model comprises an equivalent circuit model, an electrochemical model, and a thermal model, wherein the equivalent circuit model, the electrochemical model, and the thermal model are coupled.
 13. The electronic device as claimed in claim 11, wherein the at least one parameter pertaining to a battery cell, among the plurality of battery cells comprises a State of Charge (SOC) of the battery cell, capacity of the battery cell, voltage drop across terminals of the battery cell, current flowing through the battery cell, ambient temperature of the battery cell, and surface temperature of the battery cell.
 14. The electronic device as claimed in claim 11, wherein the at least one value of the at least one parameter pertaining to a battery cell, among the plurality of battery cells, is determined based on at least one of operating current fed to the battery pack, at least one electrochemical parameter fed to the battery pack, at least one thermal parameter fed to the battery pack, internal resistance of the battery cell, and connection resistance of the battery cell.
 15. The electronic device as claimed in claim 11, wherein the battery pack comprises a plurality of modules connected in series, wherein each of the plurality of modules comprises a plurality of branches connected in parallel, wherein each of the plurality of branches comprises a battery cell.
 16. The electronic device as claimed in claim 13, wherein the uptime of the battery pack includes an uptime of a battery cell in a branch of a module, wherein a value of the uptime of the battery cell is lowest amongst values of uptimes of a plurality of battery cells in the plurality of branches of each of the plurality of modules, wherein the value of the uptime of the battery cell is based on the SOC of the battery cell, capacity of the battery cell, and current flowing through the battery cell.
 17. The electronic device as claimed in claim 13, wherein the remaining capacity of the battery pack includes a remaining capacity of a battery cell in a branch of a module, wherein a value of the remaining capacity of the battery cell is lowest among values of remaining capacities of a plurality of battery cells in the plurality of branches of each of the plurality of modules, wherein the value of the remaining capacity of the battery cell is based on the SOC of the battery cell, capacity of the battery cell, current flowing through the battery cell, and current flowing in all branches of the module.
 18. The electronic device as claimed in claim 13, wherein the chargeable capacity of the battery pack includes a chargeable capacity of a battery cell in a branch of a module, wherein value of the chargeable capacity of the battery cell is lowest among values of chargeable capacities of a plurality of battery cells in the plurality of branches of each of the plurality of modules, wherein the value of the chargeable capacity of the battery cell is based on the SOC of the battery cell, capacity of the battery cell, current flowing through the battery cell, and current flowing in all branches of the module.
 19. The electronic device as claimed in claim 11, wherein the at least one processor is further configured to compute a State of Charge (SOC) of the battery pack, based on the remaining capacity of the battery pack and a total capacity of the battery pack.
 20. An electronic device comprising: a battery pack; and at least one processor configured to: measure a capacity of the battery pack based on input local current variations that occur during charging and discharge operations due to variations in cell internal resistances, capacities, and cell-to-cell temperatures; calculate local cell currents using an electrical equivalent circuit model; calculate real time cell capacities and State of Charges (SOCs) using cell electro-chemical and thermal model; and estimate a battery pack uptime, usable capacity and the chargeable capacity of the battery pack using a physics based model to determine SOC of the battery pack. 